LEP
5.1.04
Planck’s “quantum of action” from photoelectric effect
(line separation by interference filters)
PHYWE series of publications • Laboratory Experiments • Physics • PHYWE SYSTEME GMBH • 37070 Göttingen, Germany 25104 1
Related topics
External photoelectric effect, work function, absorption, photon
energy, anode, cathode.
Principle and task
A potassium photo-cell is illuminated with light of different
wavelengths. Planck’s quantum of action, or Planck’s constant
(h), is determined from the photoelectric voltages meas-
ured.
Equipment
Photocell, for h-det., w. housing 06778.00 1
Interference filters, set of 3 08461.00 1
Interference filters, set of 2 08463.00 1
Experiment lamp 6 11615.05 1
Spectral lamp Hg 100, pico 9 base 08120.14 1
Power supply for spectral lamps 13662.93 1
Mounting plate R, 32 cmϫ21 cm 13001.00 1
Universal measuring amplifier 13626.93 1
Digital multimeter 07134.00 1
Screened cable, BNC, l 300 mm 07542.10 1
Connecting cord, 250 mm, red 07360.01 1
Connecting cord, 250 mm, blue 07360.04 1
Problems
To determine Planck’s quantum of action from the photoelectric
voltages measured at different wavelengths.
Set-up and procedure
The experimental set-up is as shown in Fig. 1. The interference
filters are fitted one after the other to the light entrance
of the photo-cell.
The measuring amplifier is used in the following way
– Electrometer Re ≥ 1013
⍀
– Amplification: 100
– Time constant: 0
– Voltmeter: DC 2V
The high-impendance input of the measuring amplifier is
discharged via the ‘zero’ button between measurements.
Theory and evaluation
Half of the inside of the high-vacuum photo-cell is a metalcoated
cathode. The anular anode is opposite the cathode.
R
Fig. 1: Experimental set-up for determining Planck’s quantum of action.
LEP
5.1.04
Planck’s “quantum of action” from photoelectric effect
(line separation by interference filters)
25104 PHYWE series of publications • Laboratory Experiments • Physics • PHYWE SYSTEME GMBH • 37070 Göttingen, Germany2
If a photon of frequency f strikes the cathode, then an electron
can be ejected from the metal (external photoelectric effect) if
there is sufficient energy.
Some of the electrons thus ejected reach the (unilluminated)
anode so that a voltage is set up between anode and cathode,
which reaches the limiting value U after a short (charging)
time. The electrons can only run counter to the electric field
set up by the voltage U if they have the maximum kinetic energy,
determined by the light frequency,
hf – A =
m
v2
(Einstein equation),
where A = work function from the cathode surface, v = electron
velocity, m = rest mass of the electron.
Electrons will thus only reach the anode as long as their energy
in the electric field is equal to the kinetic energy:
eU =
m
v2
with e = electron charge = 1.602 · 10-19 As
An additional contact potential ␾ occurs because the surfaces
of the anode and cathode are different:
eU + ␾ =
m
v2
If we assume that A and ␾ are independent of the frequency,
then a linear relationship exists between the voltage U (to be
measured at high impedance) and the light frequency f:
U = –
A + ␾
+
h
f
If we assume U = a + bf to the values measured in Fig. 2 we
obtain:
h = 6.7 ± 0.3 · 10-34 Js
Literature value: h = 6.62 · 10-34 Js.
ee
2
2
2
R
Fig. 2: Voltage of the photo-cell as a function of the frequency
of the irradiated light.